We develop infinitesimally robust statistical procedures for general diffusion processes. We first prove existence and uniqueness of the times series influence function of conditionally unbiased M-estimators for ergodic and stationary diffusions, under weak conditions on the (martingale) estimating function used. We then characterize the robustness of M-estimators for diffusions and derive a class of conditionally unbiased optimal robust estimators. To compute these estimators, we propose a general algorithm, which exploits approximation methods for diffusions in the computation of the robust estimating function. Monte Carlo simulation shows a good performance of our robust estimators and an application to the robust estimation of the exchange rate dynamics within a target zone illustrates the methodology in a real-data application
We develop a discrete-time stochastic volatility option pricing model, which exploits the information contained in high-frequency data. The Realized Volatility (RV) is used as a proxy of the unobservable log-returns volatility. We model its dynamics by a simple but effective (pseudo) long memory process, the Heterogeneous Auto-Regressive Gamma with Leverage (HARGL) process. Both the discrete-time specification and the use of the RV allow us to easily estimate the model using observed historical data. Assuming a standard, exponentially affine stochastic discount factor, we obtain a fully analytic change of measure. An extensive empirical analysis of S&P 500 index options illustrates that our approach significantly outperforms competing time-varying (i.e. GARCH-type) and stochastic volatility pricing models. The pricing improvement can be ascribed to: (i) the direct use of the RV, which provides a precise and fast-adapting measure of the unobserved underlying volatility; and (ii) the specification of our model, which, on the one hand, is able to accurately reproduce the volatility persistence and, on the other hand, provides the necessary smoothing of the noise present in the RV dynamics.
Research on food decision making is often based on the assumption that people take many different aspects into account and weight and add them according to their personally assessed importance. Yet there is a growing body of research suggesting that people's decisions can often be better described by simple heuristics—rules of thumb that people use to make choices based on only a few important pieces of information. To test empirically whether a simple heuristic is able to account for individual food decisions, we ran a computerized experiment in which participants (N=50) repeatedly chose between pairs of 20 lunch dishes that were sampled from a local food court. A questionnaire assessed individual importance weights as well as evaluation ratings of each lunch dish on nine different factors. Our results show that a simple lexicographic heuristic that only considers each participant's most important factors is as good at predicting participants’ food choices as a weighted additive model that takes all factors into account. This result questions the adequacy of weighted additive models as sole descriptions of human decision making in the food domain and provides evidence that food choices may instead be based on simple heuristics.
We use the database leak of Mt. Gox exchange to analyze the dynamics of the price of bitcoin from June 2011 to November 2013. This gives us a rare opportunity to study an emerging retail-focused, highly speculative and unregulated market with trader identifiers at a tick transaction level. Jumps are frequent events and they cluster in time. The order flow imbalance and the preponderance of aggressive traders, as well as a widening of the bid-ask spread predict them. Jumps have short-term positive impact on market activity and illiquidity and see a persistent change in the price.
